I "inQuiry Almanack" - Minutes from ME - May, 1997
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Minutes from ME

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MAYTIME MEASURING

Now that bright, warm weather has returned to Pennsylvania we like to do outdoor math and science as much as possible. Being so happy to see the new Springtime GROWTH, we get feverish and simply cannot resist ... we want to measure stuff !

Enjoying the sunlight leads to investigation of the shadows it produces, so we begin with the famous exercise of estimating a tree's height by comparing the length of its shadow with the length of our own shadow.

Anne Measures!

(This is a "generic", diagram created with PAINTBRUSH software. Each student makes a unique, personal copy by changing the particular measurements he or she made and printing or saving the individual result to a disk.)

In the diagram above:

Anne's shadow is 40 inches long.
Anne is 44 inches tall.
The tree's shadow is 132 inches,or 13 feet, long.
Then by simple ratio:

Tree Height = Tree Shadow Length multiplied by (Anne's actual height divided by her shadow length)

This measurement method works well as we choose various neighborhood trees, in fact it often works too well. Our tree-filled state lives up to its "PENN'S WOODS" title. Frequently, the many trees crowd so close to each other that separating their shadows or avoiding interfering shadows is perplexing. So for simpler exercises we can switch to other measurement candidates which stand in isolation such as goalposts, flagpoles, single buildings, etc.

Measuring becomes most meaningful when the results are displayed, and a map or a chart shows the results of our group project well. So we make a map showing our various measurements.

Using a simple graphics program, such as PAINTBRUSH, we begin with a screenful of green; the main computer helper adds the path and field line markings and then each team adds its tree, fence, etc. with measurement values. Now we can print out and display the combined group project.

Group Map.

Unfortunately there are times when the weather does not cooperate and we must measure indoors. However with a few simple substitutions to the basic plan - teacher for trees, hallways for fences, Voila! we have an alternative measuring project. The resulting map looks like this:

Indoors!

Some other linear quantity questions are worth trying:

The shortest way to the playground door?
The longest way to the same door (without retracing steps)?
Is Reid's desk closer to the door?
Or is Madeline's closer?As the crow flies? or as the crow walks?
The width of a desk, the width of a person, the width of a classroom, how to fit it all in?
Is our classroom closer to the Science Lab or the Art room?

Arbor Day in Pennsylvania falls on the last Friday in April, a special time to celebrate, and measure, our trees.

To learn about an ancient and amazingly accurate scaling estimate check ERATOSTHANES PROJECT - CIRCUMFERENCE OF THE WORLD.

I acknowledge the measured inspiration from my daughter, AL, in devising these mathematical pursuits.

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